Once again, the procedure is to ask the fish seller for the type of seafood you want. You can ask by weight or by piece. They will clean the fish for you, but will probably leave the head on.
If you don't know which fish come from the Mediterranean, I suggest you look at the gallery of fish pictures in Kyle Phillips excellent La Galleria del Pesce - Photos from Italian Fish Markets. Not only will you see the primary fish available in Italy, Kyle gives recipes for each one. This is very useful information if you'll be staying in Italy a while.
An excursion into larger fish markets can be an eye-opening experience. Cagliari, Sardinia has a whole floor of its covered market devoted to fish, and it's amazing the number of things that come from the sea around Sardinia. It's like going to the aquarium but it's free and the fish are, well, dead. (Just don't get in the way of real commerce if you're just rubbernecking the markets). See Pictures of Cagliari Fish Market